**Euclidean Distance**

In mathematics, the Euclidean distance or Euclidean metric is the “ordinary” distance between two points that one would measure with a ruler, and is given by the Pythagorean formula. By using this formula as distance, Euclidean space (or even any inner product space) becomes a metric space. The associated norm is called the Euclidean norm. … **Vector Quantised-Variational AutoEncoder (VQ-VAE)**

Learning useful representations without supervision remains a key challenge in machine learning. In this paper, we propose a simple yet powerful generative model that learns such discrete representations. Our model, the Vector Quantised-Variational AutoEncoder (VQ-VAE), differs from VAEs in two key ways: the encoder network outputs discrete, rather than continuous, codes; and the prior is learnt rather than static. In order to learn a discrete latent representation, we incorporate ideas from vector quantisation (VQ). Using the VQ method allows the model to circumvent issues of ‘posterior collapse’ — where the latents are ignored when they are paired with a powerful autoregressive decoder — typically observed in the VAE framework. Pairing these representations with an autoregressive prior, the model can generate high quality images, videos, and speech as well as doing high quality speaker conversion and unsupervised learning of phonemes, providing further evidence of the utility of the learnt representations. … **Unsupervised Generative Adversarial Cross-Modal Hashing (UGACH)**

Cross-modal hashing aims to map heterogeneous multimedia data into a common Hamming space, which can realize fast and flexible retrieval across different modalities. Unsupervised cross-modal hashing is more flexible and applicable than supervised methods, since no intensive labeling work is involved. However, existing unsupervised methods learn hashing functions by preserving inter and intra correlations, while ignoring the underlying manifold structure across different modalities, which is extremely helpful to capture meaningful nearest neighbors of different modalities for cross-modal retrieval. To address the above problem, in this paper we propose an Unsupervised Generative Adversarial Cross-modal Hashing approach (UGACH), which makes full use of GAN’s ability for unsupervised representation learning to exploit the underlying manifold structure of cross-modal data. The main contributions can be summarized as follows: (1) We propose a generative adversarial network to model cross-modal hashing in an unsupervised fashion. In the proposed UGACH, given a data of one modality, the generative model tries to fit the distribution over the manifold structure, and select informative data of another modality to challenge the discriminative model. The discriminative model learns to distinguish the generated data and the true positive data sampled from correlation graph to achieve better retrieval accuracy. These two models are trained in an adversarial way to improve each other and promote hashing function learning. (2) We propose a correlation graph based approach to capture the underlying manifold structure across different modalities, so that data of different modalities but within the same manifold can have smaller Hamming distance and promote retrieval accuracy. Extensive experiments compared with 6 state-of-the-art methods verify the effectiveness of our proposed approach. …

# If you did not already know

**10**
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Feb 2018

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